This is in response to David C.
David, I'll discuss your last question first. I don't know what you mean by a
'20:1 choke point' at the antenna feed point. If you mean a 20:1 mismatch at the
feed point, then the answer is no, there is NOT a profound real-world loss when
a low-loss feed line, such as open-wire, or ladder line is used with an antenna
tuner. The actual loss in such a case is so small that the person at the
receiving end cannot distinguish between it and a case where the SWR is 1:1.
So now we'll go back to the first part of your posting.
David, reflected power not being lost power is not a paper theory. It is
measured every day with SWR indicators that indicate forward and reflected
power. If the SWR indicator is in a line with a mismatched termination of 2:1,
the SWR is 2:1, and If a transmitter were first adjusted to deliver 100 watts
into a matched line we know the SWR is 1:1, and forward power of 100 watts will
be indicated. If the line is now terminated with a 2:1 mismatch the reflected
power will be 11.1 watts. When the antenna tuner is adjusted to show a 1:1 SWR
at the input, the impedance at the input will be 50 ohms resistive, which
indicates that no reflected power is traveling rearward past the input of the
tuner. The reason is that, when the tuner is so tuned, it totally re-reflects
the reflected power, adding it directly to the power from the transmitter. Thus
the total forward power is now 111.1 watts, which will be so indicated on the
SWR-power meter. When the meter is reversed to read reflected power it will
indicate 11.1 watts. Conclusion: forward power is equal to the source power plus
the reflected power. The values of power I've used here are demonstrative, but
are overly simplified, but I will explain how the real values are obtained
later. (We'll discover that the difference is small.)
David, using a pipe containing water is an invalid analogy, because water can't
flow in two directions in a pipe. However, electromagnetic energy can travel in
both directions on a transmission line simultaneously, just as it does in fsree
space. The forward waves travel toward the load, and the reflected waves travel
toward the antenna tuner. As the two waves slide past each other they produce
the standing waves by alternately reinforcing and canceling each other. On
re-reflection at the tuner the two waves emerge in phase, and the re-reflected
wave adds to the source wave, thus enlarging the source wave into the total
forward wave. As a result the power reflected at the mismatched antenna adds to
the source wave at the tuner, only to be reflected again at the mismatch,
leaving the 100 watts delivered by the transmitter to be absorbed and radiated
by the antenna.
Now to determine the real values of forward and reflected power when the
mismatch is 2:1. The resulting voltage reflection coefficient is 1/3 = 0.33333.
The power reflection coefficient is the square of the voltage reflection
coefficient, or 0.1111. On the first cycle of energy 100 watts reaches the 2:1
mismatch, and 11.11 %, or 11.11 watts is reflected back to the tuner, where it
is totally re-reflected. Thus on the second cycle the total forward power is 100
+ 11.11 watts, or 111.11 watts. But now 11.11 % of 111.11 watts is reflected,
which is 12.345 watts, which on return to the tuner it adds to the 100 watts
from the transmitter, making the forward power on the second cycle 112.345
watts. After several more cycles the build up of power will reach the steady
state-value of 1/1 - 0.11111, which equals 1.125. Therefore, the total forward
power with a 2:1 mismatched termination will be 100 x 1.125 = 112.5 watts, and
the reflected power will be 12.5 watts. These calculations assume lossless line.
However, the attenuation in the low-loss lines we use in practice is so low that
the values I've shown are not significantly higher than the real values you'll
find on your SWR-power meters. In other words, the difference between the values
we obtain in the real world and those I've presented here are so small that they
could not be detected at the receiving end.
To respond to your suggestion that we have a perpetual-motion machine, let me
remind you that all the power that is absorbed and radiated by the antenna comes
from the transmitter, with only insignificant losses in the tuner and the
transmission line. That is why we buy the lowest loss line possible, and keep it
as short as possible.
David, I hope this answers your questions.
73, Walt Maxwell, W2DU
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